Space of modular forms of level 310 and weight 2

• Label: 310.2
• Level: 310
• Weight: 2
• Dimension: 881
• Nonzero newspaces: 12
• Newform subspaces: 31
• Sturm bound: 11520
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 31 \)
Sturm bound:			\(11520\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(310))\).

	Total	New	Old
Modular forms	3120	881	2239
Cusp forms	2641	881	1760
Eisenstein series	479	0	479

Trace form

881 * q + q^2 + 4 * q^3 + q^4 + q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 + 4 * q^15 + q^16 + 18 * q^17 + 13 * q^18 + 20 * q^19 + q^20 + 12 * q^21 - 48 * q^22 - 36 * q^23 + 4 * q^24 - 19 * q^25 - 46 * q^26 - 140 * q^27 - 72 * q^28 - 90 * q^29 - 56 * q^30 - 89 * q^31 + q^32 - 72 * q^33 - 102 * q^34 - 52 * q^35 - 67 * q^36 - 142 * q^37 - 40 * q^38 - 84 * q^39 + q^40 - 18 * q^41 - 28 * q^42 + 24 * q^43 + 12 * q^44 + 13 * q^45 + 24 * q^46 + 48 * q^47 + 4 * q^48 - 3 * q^49 + q^50 - 108 * q^51 + 14 * q^52 - 6 * q^53 + 40 * q^54 - 48 * q^55 + 8 * q^56 - 100 * q^57 + 30 * q^58 + 4 * q^60 - 118 * q^61 + 31 * q^62 - 136 * q^63 + q^64 - 76 * q^65 + 48 * q^66 + 8 * q^67 + 18 * q^68 - 84 * q^69 + 8 * q^70 - 48 * q^71 + 13 * q^72 + 14 * q^73 + 38 * q^74 - 116 * q^75 - 144 * q^77 - 124 * q^78 - 60 * q^79 - 29 * q^80 - 119 * q^81 - 78 * q^82 - 336 * q^83 - 88 * q^84 - 102 * q^85 - 196 * q^86 - 120 * q^87 - 108 * q^88 - 210 * q^89 - 167 * q^90 - 148 * q^91 + 24 * q^92 - 356 * q^93 - 72 * q^94 - 220 * q^95 + 4 * q^96 - 162 * q^97 - 303 * q^98 - 144 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
310.2.a	\(\chi_{310}(1, \cdot)\)	310.2.a.a	1	1
		310.2.a.b	1
		310.2.a.c	2
		310.2.a.d	2
		310.2.a.e	3
310.2.b	\(\chi_{310}(249, \cdot)\)	310.2.b.a	8	1
		310.2.b.b	8
310.2.e	\(\chi_{310}(191, \cdot)\)	310.2.e.a	6	2
		310.2.e.b	6
		310.2.e.c	6
		310.2.e.d	6
310.2.f	\(\chi_{310}(123, \cdot)\)	310.2.f.a	32	2
310.2.h	\(\chi_{310}(101, \cdot)\)	310.2.h.a	4	4
		310.2.h.b	4
		310.2.h.c	8
		310.2.h.d	8
		310.2.h.e	8
310.2.k	\(\chi_{310}(129, \cdot)\)	310.2.k.a	32	2
310.2.n	\(\chi_{310}(39, \cdot)\)	310.2.n.a	64	4
310.2.p	\(\chi_{310}(37, \cdot)\)	310.2.p.a	64	4
310.2.q	\(\chi_{310}(41, \cdot)\)	310.2.q.a	8	8
		310.2.q.b	8
		310.2.q.c	8
		310.2.q.d	8
		310.2.q.e	8
		310.2.q.f	8
		310.2.q.g	24
		310.2.q.h	24
310.2.s	\(\chi_{310}(23, \cdot)\)	310.2.s.a	128	8
310.2.t	\(\chi_{310}(9, \cdot)\)	310.2.t.a	128	8
310.2.w	\(\chi_{310}(3, \cdot)\)	310.2.w.a	256	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)